Thermodynamic systems as extremal hypersurfaces

Abstract

We apply variational principles in the context of geometrothermodynamics. The thermodynamic phase space T and the space of equilibrium states epsilon turn out to be described by Riemannian metrics which are invariant with respect to Legendre transformations and satisfy the differential equations following from the variation of a Nambu-Goto-like action. This implies that the volume element of epsilon is an extremal and that epsilon and T are related by an embedding harmonic map. We explore the physical meaning of geodesic curves in epsilon as describing quasi-static processes that connect different equilibrium states. We present a Legendre invariant metric which is flat (curved) in the case of an ideal (van der Waals) gas and satisfies Nambu-Goto equations. The method is used to derive some new solutions which could represent particular thermodynamic systems. (C) 2010 Elsevier B.V. All rights reserved.